The present invention relates generally to the methods of recovering or extracting useful information from data containing noise or distorted by noise. More particularly, the present invention relates to recovering the real value of a stock from the stock pricing data by removing the noise associated with a stock in a stock market.
The prior art in the field of the invention does not appear to disclose any method that is similar to the method of the present invention for recovering the real value of a stock from the stock pricing data.
The closest prior art appears to reside in the three following groups of approaches to and methods of stock valuation.
The first group of the stock valuation methods is usually associated with the value investment pioneered by Benjamin Graham. Its basic concept holds that the ability of a corporation to produce earnings determines the value that a stock market attributes to the stock of the corporation. The following is an interpretation of this concept by Nelson D. Schwartz (FORTUNE, Nov. 24, 1997). Aimed at general public, in order to make his point more vivid and convincing, he describes how Graham created a Mr. Market who comes and offers to buy a candy store. xe2x80x9cSome days he""s feeling up and offers wildly high prices; other days he offers wildly low prices. But regardless of Mr. Market""s mood, the store""s current business and its future prospects are unaffected. If you were the owner of the store, you""d value it on how much cash it was throwing off, and how much you expected it to throw off in the future. You""d sell to Mr. Market only if you believed that, after taking the proceeds and putting them into an alternative investment, you""d end up with more moneyxe2x80x94not just today, but all the way down the line. The trick, of course, is predicting the cash flow of your candy store out into the future, as well as the appropriate interest rate to use in discounting itxe2x80x9d.
Given the assumption that the financial fundamentals of a corporation is the only determinant of its stock pricing in the market, the Graham""s approach to stock valuation can be defined as deterministic valuation.
Accuracy of such valuation is low because it does not properly account for the random components in both stock pricing data and financial fundamentals of a corporation.
For example, consider how Jim Jubak, a well known analyst and writer, addresses this issue in his article xe2x80x9cA Buying Panicxe2x80x9d in the April""s, 1997, WORTH magazine: xe2x80x9cFundamentals don""t count for much. It does not matter if a stock is expensive (like Merck) or outrageously expensive (like Coca-Cola), as long as the price is rising. Professional investors are torn between a desperate fear of underperforming the indexes again and knowledge that the market could trash any stock tomorrow on the smallest signs that its upward price momentum might be slowing downxe2x80x94even if the fundamentals are still soundxe2x80x9d.
Another example is by Chuck Clough, Merrill Lynch""s top strategist: xe2x80x9cStock market valuation is imperfect science. I""ve been around a long time, and I""ve used every conceivable model known to man. There are valuation models that say the market""s incredibly overvalued, and there are models that say it""s undervaluedxe2x80x9d, cited in the above-mentioned article by Nelson D. Schwartz.
The second group of the methods of stock valuation and investment analysis can be classified as a pure probabilistic approach. Harry Markowitz initiated it in 1952. A Yale Professor William N. Goetzmann in the following way represent this concept in his Web course of investment theory: xe2x80x9cFinance professor Harry Markowitz began a revolution by suggesting that the value of a security to an investor might best be evaluated by its mean, its standard deviation, and its correlation to other securities in the portfolio. This audacious suggestion amounted to ignoring a lot of information about the firmxe2x80x94its earnings, its dividend policy, its capital structure, its market, its competitorsxe2x80x94and calculating a few simple statistics.
The Markowitz model was a brilliant innovation in the science of portfolio selection. With almost a disarming sleight-of-hand, Markowitz showed us that all the information needed to choose the best portfolio for any given level of risk is contained in three simple statistics: mean, standard deviation and correlation. It suddenly appeared that you didn""t even need any fundamental information about the firm.xe2x80x9d
However, the mathematical abstracts such as the mean and the standard deviation, unable to substitute or represent the real influence of corporate financial fundamentals on stock value and return on investment. Without such a link to the real world, this approach results in statistical processing of data containing both a regular (not random) component and a pure random component. Without first dividing these parts, it is impossible to distinguish between a change caused by a trend of appreciation of the value of a stock and a random change of its price.
More generally, such a true expanding system as a stock market can not be adequately represented or described by such simple statistics as the mean (the first moment of a probability distribution) and/or the standard deviation (the second moment of a probability distribution). By definition, an expanding system is the system whose main parameters and characteristics are evolving over time. Such a system has no fixed set of probabilities or a fixed probabilities distribution, the main requirements of applying to a system those standard probabilistic procedures. Such statistics as the mean value of a variable or its standard deviation in an expanding system are becoming outdated the moment they are calculated and thus meaningless without specifying how they are influenced by the expansion of the system. When these statistics nonetheless are applied to an expanding system, this brings about a distorted picture of the system, which a prominent English statesman, Benjamin Disraeli (1804-81) summarized in the following way: xe2x80x9cThere are three kinds of lies: lies, damned lies and statisticsxe2x80x9d.
A combination of deterministic and probabilistic approaches to stock valuation (often referred to as determining the potential of appreciation of a stock) is widely represented in the prior art. Both the pricing data of a stock and fundamental data of an underlying company are processed together for selecting stocks for a portfolio of stocks aimed at surpassing a select market index. There are more and more complex computing means involved in probabilistic processing of huge arrays of these kinds of data.
U.S. Pat. No. 5,761,442 to Dean S. Barr et al. discloses a data processing system involving an artificial neural network xe2x80x9cfor estimating the appreciation potential of each security in a capital market using both fundamental and technical information about the securityxe2x80x9d.
However, though being complex and sophisticated in terms of scope of processed data, fundamentally, such data processing systems do not depart from the above-mentioned pure probabilistic approach, as both the market pricing data and fundamental data are processed using similar statistical procedures and involving traditional statistics and statistical indicators such as the standard deviation, BETA, ALPHA and others. Though declared in the Summary of the above-mentioned invention that the use of neural networks xe2x80x9cprovides the capability to capture non-linear functional relationship among input variablesxe2x80x9d, there is no proof in the invention disclosure that this kind of result is achieved, as there is no expressions, formulas or graphs in the disclosure demonstrating an actually xe2x80x9ccapturedxe2x80x9d functional relationship between the system""s variables, but a standard formula for calculating the average of the difference between two variables.
More generally, the main flaw of the systems of probabilistic processing of these kinds of arrays of data is that the processing itself is just changing the form of data representation. There is still no proof whatsoever that a new form of representing data provides new knowledge about a system. Though being able to reveal some short term recurring patterns of system""s behavior, the probabilistic processing of data has never proved to reveal long lasting relationships between system""s variables, which is a basic indication of a new knowledge about a system. In other words, the so-called black-box approach to getting new knowledge via using some statistical processing procedures typically results in a replacement of one set of numbers by another one. As a rule, the same kind of statistics, as the averaging in the above-considered patent are used to prove that the last set of numbers is better than the first one. That is why this kind of statistical data processing sometimes looks like an endless vicious circle of comparing statistical indicators, not a way to new knowledge about a system.
An alternative to the methods of probabilistic data processing and a way to new knowledge about a stock market provide the theory of measurement in expanding systems and its application to stock markets, the theory of pragmatic investment, both are developed by author of this invention. Pragmatic investment is a new technique of investment decision-making based on the knowledge about a real stock value obtained in a stock market by direct measurement. From metrological point of view, a stock market acts as a gigantic transducer transforming its inputs in the form of bid-ask prices into the output containing the real value of a stock. The main mathematical instrument of the theory of measurement in expanding systems is differential-intermittent calculus (DI-calculus), which is a kind of differential calculus for functions that are not differentiable, i.e. not having a derivative, in the strict classical meaning of this notion. DI-calculus enables an analyst to distinguish between changes in an expanding system caused by its expansion and random changes (fluctuations). For a stock market, the first is interpreted as the trend of appreciation of an investment in a stock, while the last represents the risk of an investment in a stock. The DI-calculus is a private property of author of this invention. The elements of DI-calculus relevant to the subject matter of this invention are briefly explained in the section xe2x80x9cDetailed Description of the Inventionxe2x80x9d.
The third group of stock valuation approaches is represented by the method of moving average applied to stock pricing data (Wall Street Analyst. User""s Manual, Omega Research Inc. Miami, Fla., 1995, p. 250): xe2x80x9cThe Moving Average indicator is a simple average of the prices of the selected range days. It is probably the most well known, and widely used, technical indicator in existence. The indicator plots the moving average for the price and length chosen.xe2x80x9d
Though that usually remains unnoticed, the method of moving average is, in fact, an attempt of getting information about a stock value by direct measurement.
Generally, measurement can be defined as a technique of detecting and quantifying a useful signal obscured or distorted by a random variable interfering the measurement process; this random variable is usually referred to as noise.
Implicitly, the method of moving average deals with the following measurement model:
y=s+nxe2x80x83xe2x80x83(1)
where y is an available for observation mixture of a useful signal s and noise n, the both are unknown.
Assuming that noise is a random function of time averaging out to zero, the moving average measurement result Y is represented by the following expression:
Y=Average(y)=Average(s+n)=Average(s)xe2x80x83xe2x80x83(2)
If the Average(s) differs from zero, this method provides a possibility to detect a useful signal s.
Unfortunately, this method distorts the important characteristics of the s-signal, as the s-signal and the Average(s) are different functions of time.
To prove this shortcoming, let""s suppose that an s-signal is a simplest linear function of time:
s=at
The growth rate of this function is its derivative a, meaning that for every unit of an increase of the argument t, the s-signal is increasing by a units.
In this case, the moving average method provides the following measurement result:
Y=Average(y)=Average(at+n)=Average (at)=0.5at 
The growth rate of the measurement result is 0.5a, that is, just half of the growth rate of the original s-signal.
Even worse are the distortions of the s-signal when it grows faster than does a linear function. For example, if s=t2, the growth rate of this function is 2t, its acceleration, that is the second derivative, equals 2. The moving average measurement result will show a function having a 0.67t growth rate and a close to zero acceleration.
To reduce or eliminate these distortions of the method of moving average, the simple averaging procedure should be improved in a way that would account for expected features of a useful signal associated with a source of its origin. In the case of measurement of the real stock value that means that the financial fundamentals of an underlying company should be reflected in a measurement result.
Thus, by definition, the real stock value is the value of a stock obtained by direct measurement from data collected in the stock market under the condition that the measurement result reflects financial fundamentals of an underlying company.
Though the above-mentioned definition of direct measurement is applicable to such a social system as a stock market in almost the same way as it does to physical objects and systems, there are some important differences between these systems, which should be embraced by key notions and definitions. For a stock market, the notion of measurement is modified to the notion of recovering the real stock value for the following reason.
One of the definitions of the word xe2x80x9crecoverxe2x80x9d provided by the American Heritage Dictionary of English Language (AHDEL), Third Edition, reads: xe2x80x9cTo procure (usable substance, such as metal) from unusable substance, such as ore or wastexe2x80x9d. In our case, the xe2x80x9cusable substancexe2x80x9d is the real value of a stock xe2x80x9cprocuredxe2x80x9d (got by special efforts, obtained or acquiredxe2x80x94AHDEL) from the xe2x80x9craw materialxe2x80x9d of pricing data of the stock collected in a stock market.
The important difference between xe2x80x9cmeasurementxe2x80x9d and xe2x80x9crecoveringxe2x80x9d is that after getting a useful signal as a measurement result it is usually not important what were the noise characteristics of a physical system where the measurement had been conducted. Contrary to that, while recovering the real value of a stock it is crucially important to get noise specifics associated with a stock as they influence investment results associated with this stock. By recovering the real stock value is actually meant separating the pricing data of a stock into two undistorted component, the real value of the stock and the noise associated with this stock, and afterward to separately analyze their characteristics.
The previously described methods of and approaches to stock valuation can provide for some assessment or estimate of the real value of a stock. However, none of them provides a method for recovering, with specified accuracy the real value of a stock from the stock pricing data collected in the real stock market.
A function of time representing the real value of a stock in a predetermined period of time herein referred to as the value function of a stock. In the terms of DI-calculus, the value function of a stock is a definite integral representing a solution of a specific differential equation. Unlike classical integral calculus where a definite integral evaluates to a number, a definite integral in DI-calculus evaluates to a function.
A random function of time representing noise associated with a stock over a predetermined period of time herein referred to as the noise wave of a stock. The true noise wave, or simply the noise wave of a stock, by definition, has the zero-averaging feature, meaning that the average from all the ordinates of the noise wave is close to zero with specified accuracy in a predetermined period of time. Otherwise, the noise wave is called a biased noise wave.
As a matter of fact, the noise wave of a stock represents all the random short term fluctuations of a stock price that are not associated with financial fundamentals of an underlying company, such that are typically caused by upgrade-downgrade manipulations, concerted efforts of shorts players, put option players, announcements of a quarter earnings meeting or not meeting analysts expectations, and many other factors that are unavoidable in a real stock market.
It is a principal object of this invention to provide a method of recovering the real value of a stock from the stock pricing data collected in a stock market.
It is a further object of this invention to provide a method for separating the noise wave of a stock from the stock pricing data collected in a stock market.
It is still a further object of this invention to provide a measure of appreciation of an investment in a stock, to provide a measure of risk of an investment in a stock, and to provide an integral indicator of investment value of a stock, for selecting individual stocks or components of a portfolio of stocks.
The method of recovering the real value of a stock from the stock pricing data collected in a stock market includes the following steps:
representing stock pricing data as a function of time, herein referred to as the pricing function of a stock, over a predetermined period of time;
approximating said pricing function of a stock by a continuous function of time of a non-negative derivative feature, herein referred to as the value function of a stock, such that investment performance of said value function of a stock differs from that of said pricing function of the stock by less than a small predetermined limit of investment performance;
computing the ordinates of a random function of time herein referred to as the noise wave of a stock, by subtracting the ordinates of said value function of a stock from the related ordinates of said pricing function of this stock and dividing the differences by the related ordinates of said value function of this stock;
interpreting said value function of a stock as a trend of appreciation of an investment in the stock;
computing the growth rate of said value function of a stock and taking it as a quantitative measure of appreciation of an investment in the stock;
computing an indicator of noise intensity associated with a stock as a function of ordinates of said noise wave of the stock and taking said indicator of noise intensity as a measure of risk of an investment in the stock;
computing an integral indicator of investment value of a stock as a function of said measure of appreciation of an investment in the stock and said measure of risk of an investment in the stock;
selecting an individual stock or a component for a portfolio of stocks based on said integral indicator of investment value of a stock such that the investment reward of the stock is superior to that of another stock, or a portfolio of stocks, or a select market index.
The value function of a stock recovered from the stock pricing data in accordance with present invention proves to be firmly linked to financial fundamentals of a related corporation, while the noise represents the randomness of the trial-and-error process of valuing stocks in a stock market. The both pieces combined in the form of the investment reward indicator provide a simple but reliable quantitative measure for comparing stock""s performance, selecting individual stocks, and allocating assets in a portfolio of stocks.
The objects and the advantages of the invention will appear more fully from the following more detailed description of the invention in conjunction with the accompanying drawings.